# Stokes Equation for Sedimentation Rate Calculation

The various factors involved in the rate of settling of the particles of a suspension are embodied in the equation of Stokes law:

dx/dt = d2 (ρi-ρe)g/18η

Where,

• dx/dt is the rate of settling,
• d is the diameter of the particles,
• ρi is the density of the particle,
• ρe is the density of the medium,
• g is the gravitational constant, and
• η is the viscosity of the medium.

A number of factors can be adjusted to enhance the physical stability of a suspension, including the diameter of the particles and the density and viscosity of the medium. The effect of changing these is illustrated in the following example:

A powder has a density of 1.3 g/mL and an average particle diameter of 2.5 μm (assuming the particles to be spheres). According to the Stokes equation, this powder will settle in water (viscosity of 1 cP assumed) at this rate:

If the particle size of the powder is reduced to 0.25 μm and water is still used as the dispersion medium, the powder will now settle at this rate:

As is evident, a decrease in particle size by a factor of 10 results in a reduction in the rate of settling by a factor of 100. This enhanced effect is a result of the d factor in the Stokes equation being squared.

Related: